Detectivity of Fe Kα Lines in Gamma-Ray Bursts by Cerenkov Line Mechanism

The Fe Kα lines in gamma-ray bursts (GRBs) produced with the Cerenkov line mechanism are studied. We theoretically predict the Fe Kα line luminosities in both the early (before 1 hour) and late (～ 1day) afterglows. Assuming about 200GRBs could be detected by Swift per year, we sampled the redshift of these GRBs using the Monte Carlo method according to the GRB formation rate derived from the statistical correlation between the spectral peak energy and the peak luminosity of GRBs. Then we obtain the Fe Kα line flux distributions of the simulated GRB sample in the early and late phases. The simulated results show that the iron line flux is relatively low, so the line detection would be still a rare event at present. In addition, our results suggest that the iron lines from GRBs could be detected in the high redshift: z～3 for the early phase and z～6 for the late phase. Therefore, it is possible that the identification of Fe Kα lines in GRBs provides a tool to directly measure redshift and to study the high-redshift GRBs in the Swift era.